Local potentials in independent-electron models

Density functional theory, exact for ground states, is commonly assumed to imply an independent-electron model in which only local potential functions appear. It has recently been shown that several paradoxes in different aspects of the theory can be resolved if this locality hypothesis is abandoned. However, the locality hypothesis itself appears to be implied by rigorous variational theory. This conflict is discussed and resolved here. The resolution involves embedding the density functional theory in an orbital functional theory whose functional derivatives are not confined to normalized ground states. The orbital Euler-Lagrange equations of this extended theory in general contain effective potentials that are linear operators acting on orbital wave functions.